Steering Gear Ratio Explanation

I read an old autosprint article that said one of the drivers driving and Formula car had two steering set ups.

One gear with 7 teeth and the other with 10 teeth. They then said that second option with 10 teeth means the driver can turn the wheel less to get more steering lock and stressed the mechanical parts more.

My questions are :

(1) Does this seem correct ?

(2) I don't know much about rack and pinion steering. But would or could the 7 or 10 teeth pinion gears be the same diameter or must they be a different diameter ?

(3) Can you use different sized pinion gears with the same rack interchange-ably or does the whole thing have to be replaced (new pinion means new rack) to change between different steering set ups for the driver.

(4) Which gear actually stresses the mechanical parts in the steering system more ? 10 teeth or 7 teeth ?

1. yes
2. if rack is the same then yes, the more teeth on the pinion means larger diameter
3. would need new housing for rack as larger diameter will mean steering shaft is further away from rack
4. no idea...calling real engineers...

To answer 4. It is reasonable to assume the driver never needs to exert maximum force on the steering wheel. The level of force is actually determined by road wheel forces, so under aany given set of cornering conditions the axial force along the rack will be the same regardless of pinion size. Tooth loading is directly proportional to rack force but a larger pinion will have more teeth in contact with the rack so individual tooth stresses will be lower. The larger pinion will also allow a more favorable tooth profile.

7 teeth is an suspiciously low count for any spur gear. Does this sound possible to any gear experts out there?

I was re reading my copy of Bastow - Car suspension and Handling because of my steering Uj problem and he points out why the pinion housing is twisted at an angle relative to the rack on many production racks.

It is not only to line up for RHD or LHD as I assumed - to get enough rack traverse with only 2.5 to 4 wheel turns you need to keep the pinion to only 5 or so teeth which implies very high root stress ( just where you dont want it!). So the pinion teeth are set at an angle across the rack to improve the tooth form with so few pinion teeth and to ensure the reaction force is across more than one tooth.

It's on pages 147 and 152 of Bastow if anybody has it.

Funnily I seem to think that most racing racks have the pinion axis at 90 degrees to the rack not twisted as Bastow implies is best

To put it another way:
- A slower ratio on straights and in high speed corners where steering angle is small. Less sensitive steering is best at high speed.
- A faster ratio in tighter turns with large steering angle. Quicker steering is useful in these conditions.

Why does larger pinion mean less force applied to the rack ? What is the equation for the applied force ?

It's not so much that you are applying a lower force to the rack, it's that the road forces acting through the rack are applying a larger torque about the steering shaft (as larger pinion means the rack is further away from the pinion axis) and so the driver must apply a larger force/torque through the steering column to compensate.

Here's how the forces get from the contact patch to the steering wheel rim, ignoring all less important factors. The lateral force at the contact patch FY acts a certain distance behind the kingpin axis, T , generating a moment MKP=T*FY. This is reacted by a force FTR in the tie rod, where FTR=MKP*steering lever arm, which is roughly the distance of the OTR to the wheel centre in side view.

In a rack and pinion we usually characterise the gear ratio as the C factor, mm of rack travel for one turn of the pinion.

rack force is the sum of the two tie rod forces.

Rack force*C/1000=2*pi*steering column torque.

steering column torque=steering wheel torque

SWT=force from one hand at rim*dia of steering wheel, if you are using both hands.

I've had a quick look at rack and pinion stuff on Google - mostly a lot of very poor, innacurate drawings, and film that shows nothing. The few racks that I've worked on have had full pinions, some straight cut, some slightly helical. This animation is simplistic, but looks OK as far as it goes.

not on an F1 car, the rack bar is only 15 ish cm or so long, and it doesnt have to move far, the wheel only goes just over half a turn each way , lock to lock , im thinking that it was a gear with teeth around 2/3 of the diameter, and the rest plain .

I've had a quick look at rack and pinion stuff on Google - mostly a lot of very poor, innacurate drawings, and film that shows nothing. The few racks that I've worked on have had full pinions, some straight cut, some slightly helical. This animation is simplistic, but looks OK as far as it goes.

Taking a look at those variable ratio rack and pinion steering mechanisms in the links provided, the one thing they all seem to have in common is an increasing gear tooth pressure angle and/or helix angle at the outer ends of its travel. Either or both of these would reduce the axial output force produced by the rack for a given input torque applied at the steering wheel, at the limits of rack travel. In fact, if the images on the Zakgear website are accurate, the rack pressure angle at the outer ends appears to be 45deg (or more). This high of a pressure angle would likely result in rack friction losses of 40% or more. If steering input effort is a concern these mechanical losses should not be ignored.